Evaluate limit as x approaches 0 of (f(2+h)-f*2)/h

$lim_{x \to 0} \frac{f (2 + h) - f \cdot 2}{h}$

Take the limit of each term.

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Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f (2 + h) - f \cdot 2}{lim_{x \to 0} h}$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f (2 + h) - lim_{x \to 0} f \cdot 2}{lim_{x \to 0} h}$

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f \cdot lim_{x \to 0} 2 + h - lim_{x \to 0} f \cdot 2}{lim_{x \to 0} h}$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f \cdot (lim_{x \to 0} 2 + lim_{x \to 0} h) - lim_{x \to 0} f \cdot 2}{lim_{x \to 0} h}$

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} f \cdot (lim_{x \to 0} 2 + lim_{x \to 0} h) - lim_{x \to 0} f \cdot lim_{x \to 0} 2}{lim_{x \to 0} h}$

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Evaluate the limit of $f$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (lim_{x \to 0} 2 + lim_{x \to 0} h) - lim_{x \to 0} f \cdot lim_{x \to 0} 2}{lim_{x \to 0} h}$

Evaluate the limit of $2$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (2 + lim_{x \to 0} h) - lim_{x \to 0} f \cdot lim_{x \to 0} 2}{lim_{x \to 0} h}$

Evaluate the limit of $h$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (2 + h) - lim_{x \to 0} f \cdot lim_{x \to 0} 2}{lim_{x \to 0} h}$

Evaluate the limit of $f$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (2 + h) - f \cdot lim_{x \to 0} 2}{lim_{x \to 0} h}$

Evaluate the limit of $2$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (2 + h) - f \cdot 2}{lim_{x \to 0} h}$

Evaluate the limit of $h$ which is constant as $x$ approaches $0$ .

$\frac{f \cdot (2 + h) - f \cdot 2}{h}$

$\frac{f (2 + h) - f \cdot 2}{h}$

Simplify the answer.

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Simplify the numerator.

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Factor $f$ out of $f \cdot (2 + h) - f \cdot 2$ .

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Factor $f$ out of $- f \cdot 2$ .

$\frac{f (2 + h) + f (- 1 \cdot 2)}{h}$

Factor $f$ out of $f (2 + h) + f (- 1 \cdot 2)$ .

$\frac{f (2 + h - 1 \cdot 2)}{h}$

Multiply $- 1$ by $2$ .

$\frac{f (2 + h - 2)}{h}$

Subtract $2$ from $2$ .

$\frac{f (h + 0)}{h}$

Add $h$ and $0$ .

$\frac{f h}{h}$

Cancel the common factor of $h$ .

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Cancel the common factor.

$\frac{f h}{h}$

Divide $f$ by $1$ .

$f$

Evaluate limit as x approaches 0 of (f(2+h)-f*2)/h

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